Editor's Introduction: Will you encounter a lot of "nonsense" questions in the interview? In fact, these problems are what we call the "Fermi problem". How to solve the "Fermi problem" in the interview? Starting from the definition of the Fermi problem, this article gives a number of examples, and gives you some suggestions on how to solve the problem of Fermi in the interview, please take a look at it.
Have you ever had a very "nonsensical" question in an interview? Like what:
How many ping-pong balls can a bus hold?
How much does a certain Xi tea in Hangzhou earn in a month?
How many planes are there in the sky in Hangzhou at the moment?
…
When faced with this kind of problem, if the interviewer does not have a certain degree of analytical thinking ability, he will often be at a loss, and then guess a number by feeling. Even if you happen to guess the correct answer, your interview will most likely be difficult to pass.
In fact, the purpose of the interviewer to ask such questions is not to want a precise answer, but to examine the interviewer's logical ability, analytical ability and ability to resist pressure, how to use limited resources, rely on experience and methods to calculate a reasonable answer.
This type of problem is called the Fermi problem in English, or the "Fermi problem."
<h1 toutiao-origin="h2" >, what is the Fermi problem</h1>
The Fermi issue was named after the Italian-American physicist Fermi. He won the Nobel Prize in Physics in 1938, and he is better known for a seemingly absurd question he threw out of thin air in a class at the University of Chicago:
"How many piano tuners are there in Chicago?"
Hearing this question, the students are at a loss, even today, I believe most people do not know how to answer.
Fermi suggested that when encountering such a seemingly huge problem, you can break down the problem into some small problems that are easy to operate and recognize, and then estimate the small problems according to guesses and assumptions.
This is the core of Fermi's thinking: logical disassembly.
Let's take a look directly at how Fermi answered this question:
Number of piano tuners = Total working hours of all piano tuners throughout the year / Annual working hours of each tuner
At this point, it is disassembled into two problems:
Total working hours of all piano tuners throughout the year = number of pianos * number of tunings per year * tuning time
The working hours of each tuner throughout the year = number of working days * daily working hours
Then we only need to estimate the number of pianos, the number of tuning times per year, the length of tuning, the number of working days, and the daily working hours, and we can deduce the final answer.
For the estimation of these basic data, Fermi has its own method of estimation. Instead of estimating it directly, it estimates the value of its upper and lower limits, making an average estimate.
<h2 toutiao-origin="h3" >1</h2>
What can be known is that there were about 3 million residents in Chicago at that time, with an average of 4 people per family (more than 4 people in the United States), then it can be concluded that there were about 750,000 families in Chicago.
How many pianos are there in such a family? Because pianos were scarce in the United States at that time, the number of families who owned pianos would not exceed 1/2, nor would it be less than 1/10, because it was estimated to be 1/3. So 75/3 = 250,000, and Chicago has about 250,000 pianos.
<h2 toutiao-origin="h3" >2. The number of times the piano is tuned per year</h2>
It can be judged from common sense that the number of times a piano needs to be tuned will not exceed 1 time in 1 year, nor will it be less than 1 time in 10 years, so it is estimated to be 1 time in 5 years. So there are 50,000 pianos in the city that need to be tuned a year.
<h2 toutiao-origin="h3" >3. Tuning duration</h2>
Judging from the workload of the tuner, the time to tune the piano once will not be less than 1 hour, not more than 5 hours, so it is estimated at 2.5 hours.
<h2 toutiao-origin="h3" >4</h2>
Working 5 days a week, there are 50 weeks a year, so it is estimated that each tuner works 250 days a year.
<h2 toutiao-origin="h3" >5</h2>
According to the general working hours, it works 8 hours a day.
<h2 toutiao-origin="h3" >6</h2>
The total working hours of all piano tuners throughout the year = 250,000 / 5 * 2.5 hours = 125,000 hours
The working hours of each tuner throughout the year = 250 days * 8 hours = 2000 hours
The number of pianists = 125,000/2,000≈ 63
Afterwards, it was verified by a phone book, and the actual statistical results were very close to Fermi's speculation.
However, there is a very important premise for Fermi estimation, that is, the mastery and estimation of data need to be supported by life experience, and it is necessary to start from actual results and common sense. It is necessary to ensure the logical relationship between the front and back levels in order to deduce the final correct answer step by step.
<h1 toutiao-origin="h2" > two, must the estimate be accurate</h1>?
Some people may question, even if your estimation logic is very reasonable, but a deviation of the data will cause the deviation of the final result, can ensure that the estimation of each data is correct?
In fact, in this series of estimation processes, there is a data concept involved: the law of averages.
The principle is that in any set of calculations, the errors caused by the estimate can cancel each other out, and the more assumptions made, the greater the probability of being canceled.
For example, some people will assume that 1/10 of the family has a piano, or they may assume that each piano needs to be tuned once a year, so that one high and one low cancel each other out.
That is, when you are hypothesizing or guessing a small event, your assumptions may be too high, and some may be too low. When the number of these "hypothetical points" is sufficient, the final error will be canceled out by each other, and the overall result will eventually appear as an average, which is the theory of the law of averages.
This is why the Fermi Estimation Method will try a hundred times and the accuracy rate is very high.
<h1 toutiao-origin="h2" >3. Case analysis</h1>
Back to the 3 questions raised at the beginning:
A classroom is full, how many people can stand?
We analyze according to the above problem solving methods, put forward a general idea, and you can also try to solve specific solutions.
Case 1: How many ping-pong balls can a bus hold?
Answer direction: number of ping-pong balls = bus volume / ping-pong volume
Case 2: How much does a Xicha store in Hangzhou have a monthly income?
Answer direction: Store revenue = the sum of revenue of each category
Case 3: How many planes are there in the sky in Hangzhou at this moment?
Answer direction: The number of aircraft at this moment = the number of airports * the number of runways * the number of aircraft taking off continuously * 2 (flying in and out)
If we are answering Fermi's questions in an interview, there are a few small points to note:
<h2 toutiao-origin="h3" >1</h2>
Ensure that both sides are on the same page and frame the issues within a specific context.
For example, ask you how many buses are there in Hangzhou? Ask how many buses there are at the moment, or how many buses there are in history.
< h2 toutiao-origin="h3" >2</h2>
Answer as many points as possible when answering, which can not only clarify your own thinking, but also allow the interviewer to clearly feel your answering process.
<h2 toutiao-origin="h3" >3</h2>
When encountering problems that really have no ideas, we must not show a helpless face, analyze the problem as much as possible, and give as many ideas as we can.
<h1 toutiao-origin="h2" >4, written at the end</h1>
In real life, we often need to make judgmental decisions in the absence of information, to make our decisions as correct as possible. Everyone's way of thinking is different, and it is not necessary to blindly pursue the right answer, what we need is the ability to solve problems.
Author: Yan Tao Sanshou, founder of Fengcheng Consulting, digital marketing expert, author of "Super User Growth"
This article was originally published by @Yan Tao Sanshou on Everyone is a Product Manager. Reproduction without permission is prohibited
The title image is from Unsplash, based on the CC0 protocol